
IM-META consistently outperforms all benchmark methods except for the Ego-Facebook dataset.

The highest gain of IM-META over the second best performer can be observed from the Douban dataset under the IC model when \(k=10\)  and \(T=60\)  (refer to Fig. REF c). In this case, NF-Only using the node metadata \(\mathcal {X}\)  performs no better than Rand due to the heavy anonymization of node features in the Douban dataset. This implies that the Siamese neural network plays a vital role in accurate network inference.

Overall, CHANGE is slightly superior to Rand, which confirms the results of a prior study [1]}.

For the Ego-Facebook dataset, all methods achieve comparable performance to that of Upper-Greedy even with a very small number of node queries, e.g., \(T=10\) . This is not surprising due to the enormous size of explored subgraphs as discussed in Section REF , which results in the inclusion of (almost) all influential nodes in any explored subgraph.

In comparing the IC and WC models, it is likely that, for the WC model, the performance gap between the two methods using node features (i.e., IM-META and NF-Only) and other two methods (i.e., Rand and CHANGE) is higher than for the IC model. This is because IM-META and NF-Only are capable of estimating the expected degree of nodes; thus, the diffusion probability can be more precisely represented in the WC model by employing such methods that make use of node features.

The performance of IM-META tends to be closer to that of Upper-Greedy when the number of seed nodes, \(k\) , is relatively smaller. As an example, in the Physics dataset, IM-META achieves about 93% of the expected influence spread resulting from Upper-Greedy by querying only 60 nodes, which accounts for 5% of the total number of nodes in the given network, when \(k=5\)  and the IC model is applied (see Fig. REF b).

Interestingly, as depicted in Figs. REF  and REF , there is a correlation between the size of explored subgraphs, \(|\mathcal {V}_t|\) , and the expected influence spread \(\sigma \) . In other words, the method achieving a higher \(|\mathcal {V}_t|\)  attains a higher \(\sigma \) .

Moreover, from Figs. REF  and REF , it is worth noting that a gap in \(|\mathcal {V}_t|\)  between IM-META and NF-Only leads to a much bigger performance gap in terms of \(\sigma \)  between the two methods. This in turn means that the accuracy of network inference significantly influences the resulting \(\sigma \) .

